MinT - Best Known (210−85, 210, s)-Nets in Base 3

Best Known (210−85, 210, s)-Nets in Base 3

(210−85, 210, 148)-Net over F₃ — Constructive and digital

Digital (125, 210, 148)-net over F₃, using

6 times m-reduction [i] based on digital (125, 216, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 108, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(210−85, 210, 188)-Net over F₃ — Digital

Digital (125, 210, 188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−85, 210, 1913)-Net in Base 3 — Upper bound on s

There is no (125, 210, 1914)-net in base 3, because

1 times m-reduction [i] would yield (125, 209, 1914)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5309 084545 283821 093577 663757 334912 578756 689028 896442 383183 055096 641199 631485 531327 442595 582361 208245 > 3²⁰⁹ [i]